Problem: Simplify the following expression: $\sqrt{80}-\sqrt{125}+\sqrt{20}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{80}-\sqrt{125}+\sqrt{20}$ $= \sqrt{16 \cdot 5}-\sqrt{25 \cdot 5}+\sqrt{4 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{5}-\sqrt{25} \cdot \sqrt{5}+\sqrt{4} \cdot \sqrt{5}$ $= 4\sqrt{5}-5\sqrt{5}+2\sqrt{5}$ Finally, simplify by combining the terms. $= ( 4 - 5 + 2 )\sqrt{5} = \sqrt{5}$